Problem: Solve for $x$ and $y$ using elimination. ${6x-2y = 18}$ ${-5x+2y = -13}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {6x-2y = 18}\thinspace$ to find $y$ ${6}{(5)}{ - 2y = 18}$ $30-2y = 18$ $30{-30} - 2y = 18{-30}$ $-2y = -12$ $\dfrac{-2y}{{-2}} = \dfrac{-12}{{-2}}$ ${y = 6}$ You can also plug ${x = 5}$ into $\thinspace {-5x+2y = -13}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ + 2y = -13}$ ${y = 6}$